A glow-worm of mass `5.0 g` emits red light `(650 nm)` with a power of `0.10 w`. Entirely in the backward direction. To what speed will it have accelerated sfter `10 y` if released into free space and assumed to live?

Options

A. `21 ms^(-1)`
B. `29 ms^(-1)`
C. `31.8 ms^(-1)`
D. `0.08 ms^(-1)`

Answer

A

Explanation

The total energy emitted in a period `tau` is `ptau`. The energy of a photon of `650 nm` light is `E=(hc)/(lambda)` with `lambda=650 nm`. The total number of photons emitted in a interval `tau` is then the total energy divided by the energy per photon.
`N=(Ptau)/(E)=(Ptau lambda)/(hc)`
DeBroglie's relation apploes to each photon and thus the total momentum imparted to the glow-worm is `p=(Nh)/lambda=(Ptaulambda)/(hc)xxh/lambda=(Ptau)/(c)`
`P=0.10 w=0.10 Js^(-1), tau=10 y, p=mv`
Hence the final speed is : `v=(Ptau)/(cm)=((0.10 Js^(-1))xx(3.16xx10^(8)))/((2.998xx10^(8)ms^(-1))xx(5.0xx10^(-3) kg))=21 ms^(-1)`